Description

Theory
2

Theory/Practice
2

Instructors

José Magalhães

Contents

1. Complements of the differential calculus in R (CP1 -29%)
- Complementation of the study of real functions of a real variable:
- Functions defined in the implicit form.
 

2. Primitive of a real function of real variable (CP2 - 21%)
- Definition and properties.
- Methods of primitive determination: by the definition; algebraic decomposition; substitution; and by parts.
 

3. Definite integral (CP3 - 25%)
- The definite concept of integral as the limit of the Riemann sum.
- Geometric interpretation.
- Properties and methods of calculation of the definite integral.
- Applications of the definite integral.
- Reference to the Improper Integral.
 

4. Numerical series (CP4 - 14%)
- Notion of succession and numerical serie.
- Series of positive and alternating terms: convergence criteria.
- Applications.
 

5. Series of functions (CP5 - 11%)
- Introduction and characterization, types of series; series of powers.
- Study of the problem of the convergence.
- Series of MacLaurin and Taylor.
- Applications.

Learning Outcomes

It is intended that students:
- Acquire an attitude and appropriate for solving engineering problems (OB1);
- Thinking and develop a solid foundation for further training curriculum unit, allowing the correct use of the techniques of differential and integral calculus in the formulation and rigorous problem solving (OB2);
- Are able to understand the concepts of number and numerical functions (polynomials), analyze its convergence and estimate errors of the approximations involved in solving the respective problems (OB3).